Carve Hole in A metal water bottle model
For the bottom of your bottle you can model it, use a Mirror modifier as it is symmetrical, give it enough topology as it will need to be bent, duplicate with an Array, then at last use a Simple Deform / Bend mode to make it turn around 360°. Apply the Array and Simple Deform and remove the doubles.



For the bottle cap it seems a bit more complicated as the cut shape doesn't deform to the center. So what you could do is create a cylinder, only keep a segment, bevel it:



Cut a hole, for example with a Boolean modifier or just some vertices displacements. Extrude downwards, fill the faces.



Create an empty at the center of the cylinder object. Give the cylinder an Array modifier > Object Offset, with the empty as Object. Rotate the empty so that it recreates a cylinder.



Give your object a Subdivision Surface modifier, bring some corrections to the topology in order to sharp the edges etc.